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Algebra and Discrete Mathematics, 2005, выпуск 4, страницы 28–35
(Mi adm318)
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RESEARCH ARTICLE
Presentations and word problem for strong semilattices of semigroups
Gonca Ayik, Hayrullah Ayik, Yu. Ünlü Çukurova University, Department of Mathematics 01330–Adana, Turkey
Аннотация:
Let $I$ be a semilattice, and $S_i(i\in I)$ be a family of disjoint semigroups. Then we prove that the strong semilattice $S=\mathcal{S} [I,S_i,\phi_{j,i}]$ of semigroups $S_i$ with homomorphisms $\phi _{j,i}:S_j\rightarrow S_i$ $(j\geq i)$ is finitely presented if and only if $I$ is finite and each $S_i$ $(i\in I)$ is finitely presented. Moreover, for a finite semilattice $I$, $S$ has a soluble word problem if and only if each $S_i$ $(i\in I)$ has a soluble word problem. Finally, we give an example of non-automatic semigroup which has a soluble word problem.
Ключевые слова:
Semigroup presentations, strong semilattices of semigroups, word problems.
Поступила в редакцию: 12.09.2005 Исправленный вариант: 15.12.2005
Образец цитирования:
Gonca Ayik, Hayrullah Ayik, Yu. Ünlü, “Presentations and word problem for strong semilattices of semigroups”, Algebra Discrete Math., 2005, no. 4, 28–35
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/adm318 https://www.mathnet.ru/rus/adm/y2005/i4/p28
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Страница аннотации: | 116 | PDF полного текста: | 59 | Первая страница: | 1 |
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